This course has two aims: firstly to provide an introduction to
(IEEE) floating-point data representation and arithmetic; and secondly
to show, how naïve
implementations of obvious mathematics can go badly wrong.
An overall implicit aim is to encourage caution when using any
floating-point value produced by a computer program.

Iteration and when to stop.
Unbounded computation may produce unbounded errors.
Solving equations by iteration and comparison to terminate it.
Newton’s method.
Idea of order of convergence.
Why summing a Taylor series is problematic (loss of all precision,
range reduction, non-examinable hint at economisation).

Ill-conditioned or chaotic problems.
Effect of changes of a few ulp in the inputs.
Conditioning number when amenable to mathematical analysis;
Monte-Carlo exploration when not.